Improved Analysis, Design and Control for

Interleaved Dual-Phase ZVS GaN-Based Totem-Pole

PFC Rectifier with Coupled Inductor

Qingyun Huang, Qingxuan ma, Ruiyng Yu,

Tianxiang Chen, Alex Q. Huang

Department of Electrical and Computer Engineering

University of Texas at Austin

Austin, USA

Zhuoran Liu

University of Chinese Academy of Sciences,

Beijing, China

Abstract—This paper proposes the improved analysis,

design and control for the interleaved dual-phase ZVS

GaN-based totem-pole PFC rectifier with coupled indu-

ctor. Traditionally, the analysis and control of the coupled-

inductor-based dual-phase totem-pole PFC are not only

complicated, but also significantly different from those of

the non-coupled-inductor-based dual-phase totem-pole

PFC. In this paper, a Δ-type circuit model for the coupled

inductor is proposed to be utilized. Based on the Δ-type

coupled inductor model, the coupled-inductor-based PFC

can be simplified as a non-coupled-inductor-based PFC

with an auxiliary inductor between the two phases. Thus,

this paper proposes to simplify all the analysis, design and

control of the coupled-inductor-based dual-phase totem-

pole PFC to those of the non-coupled-inductor-based dual-

phase totem-pole PFC with an auxiliary inductor. Based

on this novel concept, the simplified analysis, the closed-

form analytical model and the full-range ZVS control

strategy are proposed and discussed. Finally, the proposed

concepts are verified by the experimental results.

Keywords—Dual-phase interleaving; GaN Totem-pole PFC;

coupled inductor; modeling; analysis and control, ZVS; auxiliary

inductor.

I. INTRODUCTION

The electricity consumed by the datacenters and the telecommunication equipment is dramatically growing recently [1], [2]. It is predicted that by 2020, roughly 10% of the total electricity will be required for the datacenters and the telecom-munication equipment [1], [2]. Therefore, the high-efficiency and high-density switching-mode AC/DC power supplies for the datacenters and telecommunication equipment are drawing more and more attention [1], [2].

The commercial AC/DC power supplies for the datacenters and telecommunication equipment contain two conversion stages: the AC/DC power factor corrector (PFC); and the isolated DC/DC converters. The isolated DC/DC converters mostly use the LLC resonant converters due to the high

efficiency [1]. For the PFC, there are several high-performance topologies: the Boost PFC; the semi-bridgeless PFC; and the totem-pole bridgeless PFC [1]-[3].

Compared with the Boost PFC and the semi-bridgeless PFC, the totem-pole bridgeless PFC has lower conduction loss [1]-[3], [8], [9]. However, the totem-pole bridgeless PFC cannot use 650V super-junction (SJ) Si MOSFETs due to the reverse recovery issue [4]. With the emerging 650V GaN FETs, the reverse recovery issue is eliminated [1], [2], [4]-[10]. In addition, the 650V GaN FETs significantly reduce the switching loss and the driving loss, compared with the SJ Si MOSFETs [1], [2], [4]-[10]. Thus, the GaN-based totem-pole bridgeless PFC for the datacenters and telecommunication equipment is drawing more and more interests.

(a)

(b)

Fig. 1. The GaN-based dual-phase totem-pole PFC with coupled inductors:

(a) negative coupling; (b) positive coupling

978-1-5386-1180-7/18/$31.00 ©2018 IEEE 2077

−

−

−

(a) (b)

Fig. 2. Equivalent circuit models of coupled inductors: (a) Y-type model for

negative coupling; (b)Y-type model for positive coupling;

−

−

−

−

(a) (b)

Fig. 3. Equivalent circuit models of coupled inductors: (a) -type model for

negative coupling; (b) -type model for positive coupling.

The triangular current mode (TCM) zero-voltage switching (ZVS) operation can eliminate the switching turn on loss of the totem-pole PFC, while it introduces high current ripple [8]-[11]. Dual phase interleaving technique can significantly reduce the current ripple, while one more magnetic component is added [8], [11]. Therefore, the dual-phase interleaved ZVS totem-pole GaN PFC with coupled inductor [12], [13], as shown in Fig. 1, becomes an interesting solution for magnetic size reduction.

However, based on the traditional circuit models of the coupled inductor, the analysis and control of the coupled-inductor-based PFC are not only complicated, but also signify-cantly different from those of the non-coupled-inductor-based PFC [13]-[17].

Among the various circuit models for the coupled inductor, the Y-type-model is the most popular and the simplest one due to the elimination of the transformer [13]-[17]. The Y-type circuit models are shown in Fig. 2 (a), (b). The coupling coefficient is defined as

(1)

where is the mutual inductance, and is the self-inductance.

In the equivalent circuits of the Y-type model as shown in Fig. 2, there are three inductors. From C to the middle point O, the inductor is - for the negative coupling, and for the

positive coupling. From the middle point O to A or B, the inductor is for the negative coupling, and for

the positive coupling. In the equivalent circuit model of the Y-type model, is the current flowing from the middle point O

to A, and is the current flowing from the middle point O to

B. By observing the current waveforms of and as shown

in Fig. 5, there are three equivalent inductances during one

switching period. The three equivalent inductances are discussed in [13], [14], [17]. And two of them are dependent on the duty-cycles [13], [14], [17]. Thus, the analysis and control for the coupled-inductor-based PFC is quite compli-cated, especially for the AC/DC application whose duty-cycles are continuously varying.

In this paper, the -type circuit model for the coupled

inductor is proposed to be utilized. As shown in Fig. 3 (a), (b), there are three inductors in the circuit: two Boost inductors and one auxiliary inductor between two switching nodes. For the two Boost inductors, one is between C and A, and another

one is between C and B. The auxiliary inductor is

between A and B. Based on the -type circuit model for the

coupled inductor, the coupled-inductor-based PFC can be simplified as a non-coupled-inductor-based PFC with an auxiliary inductor between the two phases. Since all the voltage over the three inductors are always known, there is not any duty-cycle-dependent inductance in the analysis. Thus, all the analysis, design and control of the coupled-inductor-based PFC can be simplified as those of the non-coupled-inductor-based PFC with an auxiliary inductor. Based on this novel concept, the detailed analysis, the closed-form analytical model and the full-range ZVS control strategy are proposed.

This paper is organized as follows. In Section II, the improved modeling and the operation analysis of the coupled inductor based on the -type model are discussed. In Section

III, the closed-form analytical model and full-range ZVS control are proposed. In Section IV, the experimental verification is included. Section V concludes this paper.

II. IMPROED MODELING AND OPERATION ANALYSIS OF

COUPLED INDUCTOR

By the equivalent circuit transformation of Y-type-model, the -type equivalent circuit models are derived as shown in

Fig. 3 (a), (b). Based on this model, the coupled-inductor-based dual-phase PFC can be simplified as a non-coupled-inductor-based dual-phase PFC with an auxiliary inductor ( ) between

the two switching nodes. The two Boost inductors ( and

) and the auxiliary inductor ( ) are shown in Fig. 3 (a),

(b). To simplify the analysis, only positive half line cycle is considered. The equivalent circuit of the PFC in positive half-line cycle is shown in Fig. 4.

Fig. 4. The equivalent circuit of the coupled-inductor-based totem-pole PFC

in positive half line cycle.

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A. Inductances and Voltages

For the negative coupling, the two Boost inductors are expressed as

. (2)

The auxiliary inductor is expressed as

. (3)

is a negative inductor for the negative coupled inductor.

For the positive coupling, the two Boost inductors are expressed as

. (4)

The auxiliary inductor is expressed as

. (5)

is a positive inductor for the negative coupled inductor.

The voltage of from C to A is calculated as:

(6)

The voltage of from C to B is calculated as:

(7)

The voltage of from A to B is calculated as:

(8)

Thus, based on the -type model for the coupled inductor, all

the voltages over the inductors are known as (6)-(8). And the voltages are independent on the inductances.

B. Inductor Currents for ZVS

Based on the -type model for the coupled inductor and

the voltages over the inductors, all the inductor currents can be derived as shown in Fig. 5.

The auxiliary inductor of the negative coupled inductor

is a negative inductor. To achieve TCM ZVS for and , the

currents should fulfill the following requirements:

(9)

(a) (b)

(a) (b)

Fig. 5. Operation waveforms in the positive half line cycle: (a) D>0.5,

negative coupled inductor; (b) D<0.5, negative coupled inductor; (c) D>0.5,

positive coupled inductor; (d) D<0.5, positive coupled inductor.

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-´

-´

-´

-´

t, )

t)

(a)

-´

-´

-´

-´

t, )

t, )

t, )

t )

t )

t )

(b)

Fig. 6. The therritical current ripples under the conditions: ,

, and total power . (a) peak currents of Boost inductors

and auxiliary inductor; (b) comparison of current ripples for the input AC current .

where is the valley current of and , and is the

peak current of . This requirement means that more negative

currents are required for and of the negative coupled

inductor, compared with those of the non-coupled inductor.

On the contrary, the auxiliary inductor of the positive

coupled inductor is a positive inductor. To achieve TCM ZVS for and , the currents should fulfill the following

requirements:

(10)

This requirement means that less negative currents are required for and of the positive coupled inductor, compared with

those of the non-coupled inductor.

Based on the -type model, it is easy to analyze the ZVS

operation and conditions for the coupled inductor converter. For the negative coupled inductor, more negative currents are needed for the Boost inductors, since the auxiliary inductor is negative. For the positive coupled inductor, less negative currents are needed for the Boost inductors, since the auxiliary inductor is positive. In summary, under the same average

current conditions, to achieve ZVS, less current ripples of

and are required for positive coupled inductor compared

with those of the negative coupled inductor.

C. Input Current Ripples

Under the same ZVS conditions and the same average current conditions, the current ripples of and for positive

coupled inductors are less than those for the non-coupled inductors and the negative coupled inductors. Thus, the total input current ripples of the positive coupled inductors are much less than those of the non-coupled inductors and negative coupled inductors.

Fig. 6 shows an example of the total input current ripples for the positive coupled inductors, the negative coupled induc-tors, and the non-coupled inductors under ZVS conditions. In Fig. 6, , , and the total power

. As shown in Fig. 6, the total current ripples of

the positive coupled inductors are much less than those of the other two cases.

III. CLOSED-FORM ANALYTICAL MODEL ADN FULL-RANGE

ZVS CONTROL

To explore the full range ZVS for the coupled-inductor-based totem-pole PFC, the state plane trajectory of the inductor current and the drain to source voltage is depicted in

Fig. 7. In Fig. 7, the center of the circle is expressed as:

negative coupling (11)

positive coupling (12)

The characteristic impedance is derived as:

. (13)

Using the -type model of the coupled inductor, this paper

proposes to calculate all the currents based on the non-coupled-

Fig. 7. State plane trajectory for and

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TABLE I. THREE-STEP CALCULATIONS AND EQUATIONS FOR FULL-RANGE ZVS

Step 1: calculations of at the down side resonant

period

Step 4: calculations of with coupling

Negative coupling Positive coupling

Valley current of , Peak current of ,

Active switch on current of I1,

Valley current of L11,

Step 2: calculations of i11 under non coupling conditions ( )

Active switch on current of L11,

Peak current of L11 without coupling,

SR off current of ,

Valley current of L11 without coupling,

Active switch on time,

Step 3: calculations of the auxiliary inductor current SR switch on time,

Peak current of L12,

D>0.5 D<0.5 D>0.5 D<0.5

inductor-based dual-phase totem-pole PFC first, and then insert the currents of the auxiliary inductor into the previous

calculations. All the currents and timing information can be derived by three steps based on the following parameters: the input voltage , the output voltage , the average grid

current, , the self-inductance , the coupling coefficient ,

the drain to source capacitance of the GaN device , and the

required synchronous rectifier (SR) turn off current for

ZVS. The calculation methodology and equations are listed in Table I.

The system control strategy for full-range ZVS is shown in Fig. 8. The open loop interleaving method with turn-on instant synchronization [18] is adopted here. The SR turn on time

and the active switch turn on time can be calculated based

on Table I. The zero-crossing-detection (ZCD) signal obtained by sensing the inductor current is the synchronization signal

for the timer of the master phase. As shown in Fig. 8, the turn on instant of the master phase is the synchronization signal for the timer of the slave phase. With a half switching-period delay, the active switch of the slave phase is turned on.

IV. EXPERIMENTAL RESULTS

The prototype of the dual-phase GaN-based totem-pole PFC is shown in Fig. 9. This prototype utilizes the Navitas 650V driver-integrated GaN devices. Then, one coupled induc-tor replaces the two individual inductors. The preliminary experimental results for the negative and positive coupled inductors under DC/DC conditions are shown in Fig. 10, where

, , , . These results have

verified the proposed modeling, analysis, design, and control. ZVS can be achieved for both two phases under different conditions. The ferrite core is ELP32 with the material ML91S from Hitachi.

Fig. 8. Control strategy and modulation

Fig. 9. Prototype of the dual-phase GaN-based totem-pole PFC with coupled inductor

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(a)

(b)

(c)

(d)

Fig. 10. Test waveforms where for and , and 2A/div for

and : (a) negative coupling, ; (b) negative coupling, ; (c)

positive coupling ; (d) positive coupling .

V. CONCLUSIONS

Based on the -type coupled inductor model, this paper

proposes to simplify all the analysis, design and control of the coupled-inductor-based PFC to those of the non-coupled-inductor-based PFC with an auxiliary inductor. For the nega-

tive coupled inductor, the auxiliary inductor is a negative inductor, while for the positive coupled inductor, the auxiliary inductor is a positive inductor. All the voltages over the inductors in the -type model are always known and inde-

pendent on the inductances. To achieve ZVS, less negative currents are needed for the Boost inductors of the positive coupled inductor, compared with those of the negative coupled inductors. Thus, under the same average current conditions, to achieve ZVS, the positive-coupled-inductor-based PFC has much less grid input current ripple than the negative-coupled-inductor-based PFC. In addition, the closed-form analytical model based on the three-step-calculations is proposed in this paper. Moreover, the ZVS control strategy is also discussed in this paper. The proposed concepts are verified by the experim-ental results based on a prototype of the GaN-based dual-phase interleaved totem-pole PFC with coupled inductor.

ACKNOWLEDGMENT

This work was conducted with the use of GaN device samples donated by Navitas.

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